Find the gradient, equations and intersections of medians, altitudes and perpendicular bisectors using our knowledge of the mid-point as well as parallel and perpendicular lines.

Remember that to find the equation of a straight line you need to know its gradient and a point on the line.

In some instances you are told the value of the gradient, however there are times where you may be required to calculate the gradient using the relevant formulae or your knowledge of parallel and perpendicular lines.

Find the equation of the line through and parallel to the line with equation .

We need to use

First find the gradient of the parallel line.

Parallel lines have equal gradients.

Now we can use with and

The equation of the parallel line is or

Find the equation of the line perpendicular to where and and passing through the midpoint of AB.

Firstly find the gradient of AB.

Perpendicular lines have gradients which multiply to give -1.

- Remember, for perpendicular lines

Now that we have the gradient, we next need to find the midpoint of AB so that we have a point on the line.

Midpoint

Now we can find the equation of the line with gradient , passing through the point

If it is required for the next part of a question then multiply both sides by 26 to clear the fractions. The lowest common multiple of 2 and 13 is 26.

Therefore the equation of the line is